Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities

We consider the Cahn-Hilliard equation on manifolds with conical singularities. For appropriate initial data we show that the solution exists in the maximal $L^q$-regularity space for all times and becomes instantaneously smooth in space and time, where the maximal $L^q$-regularity is obtained in the sense of Mellin-Sobolev spaces. Moreover, we provide precise information concerning the asymptotic behavior of the solution close to the conical tips in terms of the local geometry.Comment: 26 page

Big Data as a Technology-to-think-with for Scientific Literacy

This research aimed to identify indications of scientific literacy resulting from a didactic and investigative interaction with Google Trends Big Data software by first-year students from a high-school in Novo Hamburgo, Southern Brazil. Both teaching strategies and research interpretations lie on four theoretical backgrounds. Firstly, Bunge's epistemology, which provides a thorough characterization of Science that was central to our study. Secondly, the conceptual framework of scientific literacy of Fives et al. that makes our teaching focus precise and concise, as well as supports one of our methodological tool: the SLA (scientific literacy assessment). Thirdly, the "crowdledge" construct from dos Santos, which gives meaning to our study when as it makes the development of scientific literacy itself versatile for paying attention on sociotechnological and epistemological contemporary phenomena. Finally, the learning principles from Papert's Constructionism inspired our educational activities. Our educational actions consisted of students, divided into two classes, investigating phenomena chose by them. A triangulation process to integrate quantitative and qualitative methods on the assessments results was done. The experimental design consisted in post-tests only and the experimental variable was the way of access to the world. The experimental group interacted with the world using analyses of temporal and regional plots of interest of terms or topics searched on Google. The control class did 'placebo' interactions with the world through on-site observations of bryophytes, fungus or whatever in the schoolyard. As general results of our research, a constructionist environment based on Big Data analysis showed itself as a richer strategy to develop scientific literacy, compared to a free schoolyard exploration.Comment: 23 pages, 2 figures, 8 table